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In this paper, we study the large-scale boundary regularity for the Stokessystem in periodically oscillating John domains. Our main contribution is theconstruction of boundary layer correctors of arbitrary order. This is asignificant generalization of the known results restricted to the first andsecond orders. As an application, we prove the large-scale regularity estimate,as well as a Liouville theorem, of arbitrary order for the Stokes system. Ourresults are also related to higher-order boundary layer tails and wall laws inviscous fluids over rough boundaries.

Higher-order boundary layers and regularity for Stokes systems over rough boundaries